Byward Market Cheapeats?
Khao Thai on Murray has some of the best Thai food in town, and the prices are surprisingly cheap.
Ahora Mexican on Dalhousie is great, but it's small.
Nagina Indian on Rideau @ Cumberland is good. Their buffet is fine (as buffets go), but their menu items are often fabulous. Very affordable.
Pour House/Auld Dubliner at George/Byward has great pub fare and not too expensive.
Honest Lawyer on George @ Dalhousie has great, novel, pub style food. Not too expensive, but the service often blows.
Patty Bolands, as KMary mentions, also has great food, though not nearly as good selection since they shrunk their menu by a third (or so). It's also quite a bit more expensive than the Lawyer or Pour House.
The Black Thorn Cafe at Clarence & Sussex also has great food (if you stick to the simple items; pizza/pasta) for a reasonable price.
Since you mentioned "ethnic" though, I'd try Khao Thai (http://www.khaothai.ca/dinner.htm). It says "fine dining", and the food certainly is, but it's quite laid back.
It's too bad the weather isn't patio-friendly; however, if you're into Mexican definitely try Pancho Villa on Elgin Street. Fabulous food-great service! If you'd rather eat directly in the market,I used to frequent Patty Bowland's as a starving University/College student. Awesome soups and artichoke dip! These two places are group-friendly, although because The Panch's patio isn't open, you may prefer Patty Bowland's for the ambience--fireplaces, live music upstairs etc...